18. Найдите значение выражения (\frac{3x^4}{a^5})^3 \cdot (\frac{a^6}{3x^5})^4 при a = -\frac{1}{7} и x = 0,14.

Решение: 1. (\frac{3x^4}{a^5})^3 \cdot (\frac{a^6}{3x^5})^4 = \frac{3^3x^{12}}{a^{15}} \cdot \frac{a^{24}}{3^4x^{20}} = \frac{a^{24}3^3x^{12}}{a^{15}3^4x^{20}} = \frac{a^9}{3x^8} 2. a = -\frac{1}{7}, x = 0,14 = \frac{14}{100} = \frac{7}{50} 3. \frac{a^9}{3x^8} = \frac{(-\frac{1}{7})^9}{3(\frac{7}{50})^8} = \frac{-\frac{1}{7^9}}{3(\frac{7^8}{50^8})} = \frac{-1}{7^9} \cdot \frac{50^8}{3*7^8} = \frac{-50^8}{3*7^{17}} = \frac{-3906250000000000}{3*827240261886336764177} \approx -1.57 * 10^{-6} Ответ: \frac{-50^8}{3*7^{17}}